Internally you have a set of solenoid valves which controls the water flow from your hoses. I suspect one is leaking. For now make sure you turn the water supply valve off when your done with the washer until you get it fixed.
I strongly recommend installing a sensor valve which turns off the water at the hose feeds that way if a hose lets loose you don't have a swimming pool in the basement (example unit). Also consider getting a grit filter on the waterline entering your house as it's likely something has jammed up the solenoid that flushed into it (example unit).
To isolate out which valve needs replacing, turn off the water of one side only (hot or cold) if you have a valve some where along the line during the night and see if the tub has filled up. You should be able to deduce which solenoid is bad. If you don't you'll need to get a cap to fit over one of the hose connections to isolate out which side.
obbarius, "this could be caused by a water inlet valve malfunction. The valve has a diaphragm that is electronically controlled. It closes to shut the water off when not in use. Over time the valve can accumulate sediment and debris causing the valve not to seat properly. You can try and clean the valve with vinegar to remove any sediments. Clean it with running water after.You will need to remove the valve to do this. Should the cleaning not resolve the issue, you may have to replace the valve. For that you have to open the machine from the top:"
Remove the three screws holding the top panel in place.
Disconnect the hoses and electrical connections to the water inlet valve.
Remove the mounting screws holding the water inlet valve.